Heat Kernel Estimates for Operators with Boundary Conditions

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Criterion for the Lp-dissipativity of second order differential operators with complex coefficients (2004, background): “1 Introduction Various aspects of the L-theory of semigroups generated by linear differential operators were studied in [4, 6, 2, 23, 7, 11, 21, 8, 9, 15, 19, 14, 13, 5, 10, 22, 16] et al.”
Domain Perturbation for Linear and Semi-Linear Boundary Value Problems (2008, background): “Also if p = N , then the spectrum is independent of p by [95] because of Gaussian bounds for heat kernels (see [55]).”
Lp-maximal regularity for second order Cauchy problems (2005, background): “In Arendt & ter Elst [5], Daners [ 16 ] or Hieber [21], [22], H ∞ functional calculus is proved for elliptic operators in divergence form.”
Estimates of Integral Kernels for Semigroups Associated with Second-Order Elliptic Operators with Singular Coefficients (2003, background): “The result was extended in several directions including lower-order terms, complex coefficients, different types of boundary value problems (see [1, 3, 4, 12 , 18, 21, 26] and the list is by no means complete).”